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Question
Using step-deviation method, calculate the mean marks of the following distribution.
| C.I. | 50 – 55 | 55 – 60 | 60 – 65 | 65 – 70 | 70 – 75 | 75 – 80 | 80 – 85 | 85 – 90 |
| Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |
Solution
Let the assumed mean A = 72.5
|
C.I. |
fi |
Mid-value |
A = 72.5 `bb(t = (x - A)/i)` |
fiti |
| 50 – 55 | 5 | 52.5 | –4 | –20 |
| 55 – 60 | 20 | 57.5 | –3 | –60 |
| 60 – 65 | 10 | 62.5 | –2 | –20 |
| 65 – 70 | 10 | 67.5 | –1 | –10 |
| 70 – 75 | 9 | 72.5 | 0 | 0 |
| 75 – 80 | 6 | 77.5 | 1 | 6 |
| 80 – 85 | 12 | 82.5 | 2 | 24 |
| 85 – 90 | 8 | 87.5 | 3 | 24 |
| Total | 80 | –56 |
Mean = `A + (f_it_i)/n xx i`
= `72.5 + (-56/80) xx 5`
= 72.5 – 0.7 × 5
= 72.5 – 3.5
= 69
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